In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.
The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, and does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work.
Since the forces involved (gravity and electric force) are conservative we can use conservation of energy.
The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
Ki + Ui = Kf + Uf
1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so
1/2)kx^2 = F∆d.
The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.
I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...
Hi, Everyone! This is the page(first image) from Principle of physics by resnik.
I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition?
Secondly, how did they reach...
Suppose I have some interaction potential, u(r), between two repelling particles. We will name them particles 1 and 2.
I want to find the force vectors F_12 and F_21. Would I be correct in saying that the x-component of F_12 would be given by -du/dx, y-component -du/dy etc? And to find the...
I'm stuck in a problem of a spring mass system with a pendulum attached to it as showed in the figure below:
My goal is to find the movement equation for the mass, using Lagrangian dynamics.
If the spring moves, the wire will move the same amount. Therefore, we can write the x and y position...
Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force.
The weight is simple enough ##12* 9.8=117.6N##...
Summary:: A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying 40kg of gear. How much power does he need to reach the top of the building in 55s.
So first the total mass of our system is 130 kg. Using this mass, I found the potential energy the firefighter would...
In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$
Terms in...
I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help.
The torque on a dipole can be defined as
τ=PEsinθ
The work done on a dipole to move it from an angle ##\theta_0##...
This question does not have numbers, so I'm stumped. Here's my thinking.
(I), the gain in KE is less than the loss in GPE is correct according to the key, but I think I don't understand this conceptually. Can you ask me questions to make me think about this a bit more? I can't even form...
I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...
It is my second "energy state diagram problem" and I would want to know if I am thinking correctly.
First I have done some function analysis to get a glimpse of the plot:
- no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0##
- y interception: ##U(0)=-U_0##
- even...
How would you go about calculating the work done in morphing a square current-carrying loop into a circular current-carrying loop, without change in length while maintaining the same angular orientation with an external magnetic field.
My book suggests defining P(potential energy) = M.B (dot...
a) Can we convert energy to mass (matter) in every day life?
b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?
So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m.
Then I found change in potential energy, -5.597*10^11 m.
Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...
Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B:
$$U=-\boldsymbol{\mu} \cdot \textbf{B}$$.
However, I was told that magnetic fields are non-conservative, so we can't...
Summary:: I have an assignment that is looking at how a bicycle pump is used to push air through a turbine to generate energy. I need to determine the energy input and energy created. I'm hoping I can get some direction on where to start.
The concept is straightforward. A bicycle pump of...
I know how to solve this problem when the energy at ground state is zero but I don't know how to deal with 1st excited state energy as zero.
According to me since the potential energy is zero therefore the kinetic energy must be 13.6eV according to conservation of energy.
I also know that the...
I have not clear how to solve this problem. Here it is my attempt at a solution:
Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...
So far I found the answer for a and b, but when I attempted to do the other ones I was completely lost.
A.) P= MV
M = 25g = .025kg
V = 18
.025 * 18 = .45kg*m/s
B.) KE= 1/2 mv^2
1/2 (.025)(18)^2
4.05 J
I have some conceptual questions about this task. In order to get the correct result (I checked the textbook answer) in part (a) I had to assume that the speed for each block is the same at all instants. And that if one block moves down x meters, the other one will move up that same amount of...
If for example I have two charged particles q_1 , q_2 with distance 'r' between them, then:
The potential energy that results from particle q_1 exerting force on particle q_2 is $$ k\frac{q_1 q_2}{r} $$
If I do the same process for particle q_2:
The potential energy that results...
Hello,
I'm newly discovering the world of the Energy.
My question is about the equation ##U=\int \vec{F}\times d\vec{r}=-\int \vec{F}_{s}\times d\vec{r}##.
Can you tell me what does this equation means?
Thanks!
(Throughout all my post, I will refer to “gravitational potential energy” just as “potential energy”)
Hi! I have this confusion about when is potential energy positive/negative and how it is related to how we define our axes. I think it is easier to understand my confusion with the following...
I drew a diagram for the a) part
The person is h meters high
So GPE= 100 x 9.8x h
GPE= 980h j
KE = 980h when the person hits the see saw
KE=1/2mv²
980h=0.5 x 5 x v²
Now it v²=u²+2as
For the brick going up to 10m
v = 0
u=?
a=-9.8ms-²
s=10m
u²=2 x 9.8 x 10
u=14m/s
We can assume that u=14m/s is...
Elastic Potential Energy of a Strained Body
(A) Using ## Y = \frac {stress}{strain}## we get ##F = \frac {AY}{L} * x## where ##F## is the restoring force, ##x## is the distance the body is stretched by.
Since Work = PE (spring force/ stress is conservative?)
Thus ##W = \int_{0}^{x} \frac...
A while back I thought of an issue with parallel charged plates. Imagine this: a set of opposite charged resistive plates with holes in the center. In theory, there is a finite amount of energy required to push a positive charged particle through the hole in the positive plate (in theory it...
Homework Statement
The system is released from rest with no slack in the cable and with the spring stretched 225 mm. Determine the distance s traveled by the 3.2-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2.5 kg. Assume no mechanical interference and no friction...
When I first learned about these subjects, I did what was intuitive to me and treated particles as if they carried potential energy. I would do this similarly for rigid bodies where I would also treat them as a particles with their body's mass at the center of mass. This wasn't helped by...
Hello everyone,
Any object has a gravitational potential energy as a function of the distance from the Earth (R). Does this energy depend only on the rest mass of the object; or one must take into account it's relativistic mass?
In other words, if we imagine two identical bullets on the top...
In quantum mechanics, there exist some systems where the potential energy of some particle is a Dirac delta function of position: ##V(x) = A\delta (x-x_0 )##, where ##A## is a constant with proper dimensions.
Is there any classical mechanics application of this? It would seem that if I...
Hi All,
The Potential Energy for two chemically bonding atoms is defined by ,U=1/2(k*q1*q2)/r
So it means that when the atoms approach each other then, their Potential Energy will increase.
Where am I doing wrong?
I will be thankful for help!
What is a conservative force and how do you determine the work done by it.
It is an interesting relation between the work done by such a force and the potential energy and kinetic energy of a particle.
Homework Statement
A rocket burns out at an altitude h above the Earth's surface. Its speed v0 at burnout exceeds the escape speed vesc appropriate to the burnout altitude. Show that the speed v of the rocket very far from the Earth is given by v=(v02-v2esc)1/2
Homework Equations
KEf-KEi=Ui-Uf...
Consider the classical scenario a stone falling in the Earth gravitational field.
Classically we attach a Potential Energy to the stone and using the law of conservation of (mechanical) energy we are able to evaluate the dynamic of the falling stone.
This model assume a stone in a "external"...
Homework Statement
Please look at the problem attached as a screenshot.
Homework Equations
Assuming frictionless, Ei = Ef, which means objects that are the same will end up in the same heights (so we can group A&C, B&D, and E&F).
For A&C and E&F, mgh = KE_rot + KE_trans
For B&D, it is mgh...
Homework Statement
Please look at the attached screenshot.
Homework Equations
Assuming the ramp is frictionless, Ei = Ef and thus mgh = KE ( = 1/2mv^2, which isn't really necessary here)
The Attempt at a Solution
I'm okay with all other examples except for A and C. From the answer template...
Homework Statement
Please look at the attached screenshot.
This problem is really confusing for me and I can't seem to make much sense out of it.
Homework Equations
Ei = Ef
The Attempt at a Solution
As you can see, I did get (a). (The other checkmarks, I guessed — there were only two...
Let, we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential energy of the system,but why we take the P.E of particles due to each other into count...
Homework Statement
Movers must push a piano onto a truck, the bed of which is a height 1.35 m above the ground. To do this they will use a frictionless ramp. If the piano has a mass of 1806.0 kg and the movers push it up the slope at a constant velocity, how much work do they need to do on it...
I have been doing pendulum problems lately, and I have found 2 different formulations for potential energy of a pendulum.
U=mgl(1-cos(Θ)) and U=-mglcos(Θ)
The first says U=0 when Θ=0 (at the bottom). The second has U=0 when Θ=π/2 (halfway to the top).
Both give the same equation of motion...
Homework Statement
If we lift a block with constant velocity, by applying a force mg upwards, is the work done zero?
Homework Equations
The Attempt at a Solution
The work done must be zero as the resultant force is zero, what I don't understand is how does the block get potential energy if...
Do electromagnetic waves have potential and kinetic energy like springs, strings, etc. If so how are they calculated, inter-related? What is the total energy? Are the energies fluctuating over time?
I am a physics hobbyist so generally the first answers should come with the least mathematics...